@Peter Referring to respected mathematical ideas as "garbage" is a surefire way to lose respect of your peers. I suggest you read more on these topics, e.g. here and here
@Peter I don't have the knowledge to talk about these topics in depth, in a comment I said that $\infty$ is not a number and another user pointed out that my statement is non sensical without explanation. I may be wrong and I'd like to learn. As I understand, also if we consider the compactification of the real line and the extended real line, we can't say that $\infty$ is a number.
@BillDubuque Is it wrong saying that $\infty$ is not a number?
@SineoftheTime Are cardinals "numbers?" If yes, then several sorts of infinity are numbers. Should numbers have to satisfy ring axioms? Then no, it doesn't work out for infinity sometimes. It's all highly dependent on context. The problem with something like the extended real numbers is that it invites slurring ideas of algebraic structure with topological and order structure, and one has to back up a step to think about it.
I think the statement of the post in question was a good example of someone not realizing what they were getting into.
Is there a formula to construct a Collatz (3x + 1) sequence of arbitrary length that is strictly increasing? Obviously one can do this with a strictly decreasing sequence by just taking $2^n$ but I haven't seen a way to do it with a strictly increasing sequence.
@SineoftheTime Yes. It is wrong to say "infinity is not a number".
It is also wrong to say "infinity is a number".
Both statements require some definition of what a "number" is, and what "infinity" is (and maybe what "is" is), and either statement could be true in the right context.
Is there a formula to construct a Collatz (3x + 1) sequence of arbitrary length that is strictly increasing? Obviously one can do this with a strictly decreasing sequence by just taking $2^n$ but I haven't seen a way to do it with a strictly increasing sequence.
